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arXiv · 2406.04863

Constructing $3$-Dimensional Monogenic Homogeneous Functions

Hamed Baghal Ghaffari·Jeffrey A. Hogan·Joseph D. Lakey
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Abstract

This paper is dedicated to the construction of multidimensional spherical monogenics. Firstly, we investigate the construction of monogenic functions in dimension $3$ by applying the Dirac operator to the orthonormal bases of spherical harmonics, resulting in orthogonal spherical monogenics. Additionally, we employ the reproducing kernel for monogenic functions and a specialized optimization method to derive various types of $3$-dimensional spherical harmonics and spherical monogenics.

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Hamed Baghal Ghaffari, Jeffrey A. Hogan, Joseph D. Lakey. 2024-06-07. Constructing $3$-Dimensional Monogenic Homogeneous Functions. https://arxiv.org/abs/2406.04863

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